The basis for indicating the waiting time at a station stop until the arrival of the next vehicle, in particular of a bus or a streetcar of the public transit system, is typically the instantaneous distance of the vehicle from the station stop. However, the actual driving times of vehicles that moved from this position to the station stop can also be taken into consideration. A rider of the transit system would then have a realistic idea about the waiting time until the next vehicle arrives, even in the event of a traffic congestion. Conventional waiting time prediction systems have so far been integrated into a RBL system (Computerized Operation Guide System). Such RBL systems are rather complex and expensive multi-component systems.